A note on the distribution of the number of prime factors of the integers

The Chernoff-Hoeffding bounds are fundamental probabilistic tools. An elementary approach is presented to obtain a Chernoff-type upper-tail bound for the number of prime factors of a random integer in {1, 2, . . . , n}. The method illustrates tail bounds in negatively-correlated settings. Key words: Chernoff bounds, probabilistic number theory, primes, tail bounds, dependent random variables, randomized algorithms

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Aravind Srinivasan
• Keywords: Chernoff Bounds, Chernoff-Hoeffding Bounds, Chernoff-type Upper-tail Bound, IPL 2008